Quantum Flux and Reverse Engineering of Quantum Wavefunctions

An interpretation of the probability flux is given, based on a derivation of its eigenstates and relating them to coherent state projections on a quantum wavefunction. An extended definition of the flux operator is obtained using coherent states. We present a "processed Husimi" representation, which makes decisions using many Husimi projections at each location. The processed Husimi representation reverse engineers or deconstructs the wavefunction, yielding the underlying classical ray structure. Our approach makes possible interpreting the dynamics of systems where the probability flux is uniformly zero or strongly misleading. The new technique is demonstrated by the calculation of particle flow maps of the classical dynamics underlying a quantum wavefunction.Comment: Accepted to EP

Torsional Potential Energy Surfaces of Dinitrobenzene Isomers

The torsional potential energy surfaces of 1,2-dinitrobenzene, 1,3-dinitrobenzene, and 1,4-dinitrobenzene were calculated using the B3LYP functional with 6-31G(d) basis sets. Three-dimensional energy surfaces were created, allowing each of the two C-N bonds to rotate through 64 positions. Dinitrobenzene was chosen for the study because each of the three different isomers has widely varying steric hindrances and bond hybridization, which affect the energy of each conformation of the isomers as the nitro functional groups rotate. The accuracy of the method is determined by comparison with previous theoretical and experimental results. The surfaces provide valuable insight into the mechanics of conjugated molecules. The computation of potential energy surfaces has powerful application in modeling molecular structures, making the determination of the lowest energy conformations of complex molecules far more computationally accessible

Aharonov-Casher effect in a two dimensional hole gas with spin-orbit interaction

We study the quantum interference effects induced by the Aharonov-Casher phase in a ring structure in a two-dimensional heavy hole (HH) system with spin-orbit interaction realizable in narrow asymmetric quantum wells. The influence of the spin-orbit interaction strength on the transport is investigated analytically. These analytical results allow us to explain the interference effects as a signature of the Aharonov-Casher Berry phases. Unlike previous studies on the electron two-dimensional Rashba systems, we find that the frequency of conductance modulations as a function of the spin-orbit strength is not constant but increases for larger spin-orbit splittings. In the limit of thin channel rings (width smaller than Fermi wavelength), we find that the spin-orbit splitting can be greatly increased due to quantization in the radial direction. We also study the influence of magnetic field considering both limits of small and large Zeeman splittings.Comment: 6 pages, 4 figure

Palatini versus metric formulation in higher curvature gravity

We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that there is a class of theories for which the two formalisms are equivalent. This class contains the Palatini version of Lovelock theory, but also more Lagrangians that are not Lovelock, but respect certain symmetries. For the general case, we find that imposing the Levi-Civita connection as an Ansatz, the Palatini formalism is contained within the metric formalism, in the sense that any solution of the former also appears as a solution of the latter, but not necessarily the other way around. Finally we give the conditions the solutions of the metric equations should satisfy in order to solve the Palatini equations.Comment: 13 pages, latex. V2: reference added, major changes in section 3, conclusions partially correcte

Optical Control of Entangled States in Quantum Wells

We present theory and calculations for coherent high-fidelity quantum control of many-particle states in semiconductor quantum wells. We show that coupling a two-electron double quantum dot to a terahertz optical source enables targeted excitations that are one to two orders of magnitude faster and significantly more accurate than those obtained with electric gates. The optical fields subject to physical constraints are obtained through quantum optimal control theory that we apply in conjunction with the numerically exact solution of the time-dependent Schrodinger equation. Our ability to coherently control arbitrary two-electron states, and to maximize the entanglement, opens up further perspectives in solid-state quantum information

Control of Josephson current by Aharonov-Casher Phase in a Rashba Ring

We study the interference effect induced by the Aharonov-Casher phase on the Josephson current through a semiconducting ring attached to superconducting leads. Using a 1D model that incorporates spin-orbit coupling in the semiconducting ring, we calculate the Andreev levels analytically and numerically, and predict oscillations of the Josephson current due to the AC phase. This result is valid from the point contact limit to the long channel length limit, as defined by the ratio of the junction length and the BCS healing length. We show in the long channel length limit that the impurity scattering has no effect on the oscillation of the Josephson current, in contrast to the case of conductivity oscillations in a spin-orbit coupled ring system attached to normal leads where impurity scattering reduces the amplitude of oscillations. Our results suggest a new scheme to measure the AC phase with, in principle, higher sensitivity. In addition, this effect allows for control of the Josephson current through the gate voltage tuned AC phase.Comment: 12pages, 8 figure

Husimi Maps in Lattices

We build upon previous work that used coherent states as a measurement of the local phase space and extended the flux operator by adapting the Husimi projection to produce a vector field called the Husimi map. In this article, we extend its definition from continuous systems to lattices. This requires making several adjustments to incorporate effects such as group velocity and multiple bands. Several phenomena which uniquely occur in lattice systems, like group-velocity warping and internal Bragg diffraction, are explained and demonstrated using Husimi maps. We also show that scattering points between bands and valleys can be identified in the divergence of the Husimi map

On the Hagedorn Behaviour of Singular Scale-Invariant Plane Waves

As a step towards understanding the properties of string theory in time-dependent and singular spacetimes, we study the divergence of density operators for string ensembles in singular scale-invariant plane waves, i.e. those plane waves that arise as the Penrose limits of generic power-law spacetime singularities. We show that the scale invariance implies that the Hagedorn behaviour of bosonic and supersymmetric strings in these backgrounds, even with the inclusion of RR or NS fields, is the same as that of strings in flat space. This is in marked contrast to the behaviour of strings in the BFHP plane wave which exhibit quantitatively and qualitatively different thermodynamic properties.Comment: 15 pages, LaTeX2e, v2: JHEP3.cls, one reference adde

Aharonov-Casher and spin Hall effects in two-dimensional mesoscopic ring structures with strong spin-orbit interaction

We study the quantum interference effects induced by the Aharonov-Casher phase in asymmetrically confined two-dimensional electron and heavy-hole ring structures systems taking into account the electrically tunable spin-orbit (SO) interaction. We have calculated the non-adiabatic transport properties of charges (heavy-holes and electrons) in two-probe thin ring structures and compare how the form of the SO coupling of the carries affects it. We show that both the SO splitting of the bands and the carrier density can be used to modulate the conductance through the ring. We show that the dependence on carrier density is due to the backscattering from the leads which shows pronounce resonances when the Fermi energy is close to the eigenenergy of the ring. We also calculate the spin Hall conductivity and longitudinal conductivity in four-probe rings as a function of the carrier density and SO interaction, demonstrating that for heavy-hole carriers both conductivities are larger than for electrons. Finally, we investigate the transport properties of mesoscopic rings with spatially inhomogeneous SO coupling. We show that devices with inhomogeneous SO interaction exhibit an electrically controlled spin-flipping mechanism.Comment: 10 pages and 7 figure